WiiLi.org has reported the following:
"Flash player version, that is embedded in the Internet Channel, is affected by the vulnerability in the Flash video handling code that reportedly allows of executing native code."

http://www.wiili.org/index.php/Executing_Our_Code/Flv_vuln

The related CVE reference is
http://cve.mitre.org/cgi-bin/cvename.cgi?name=CVE-2007-3456

henke37 of WiiLi.org has confirmed the vulnerability on the Nintendo Wii.

From the report of ComputerAndVideoGames.com:
"This could, among other things, lead to the creation of game emulators on the console"